Multipurpose piezoelectric transducer system



Feb. 14, 1967 A. 0. SYKES 3,304,534

MULTIPURPOSE PIEZOELECTRIC TRANSDUCER SYSTEM Original Filed Feb. 27,1963 4 Sheets-Sheet 1 AXIS OF SYMMETRY lilll II FIGZ.

INVENTOR Fl 21 26 26a ALAN o. SYKES ATTY.

Feb. 14, 1967 A. o. SYKES 3,304,534

MULTIPURPOSE PIEZOELECTRIC TRANSDUCER SYSTEM Original Filed Feb. 27,1963 4 Sheets-Sheet 2 INVENTOR ALAN O. SYKES B Q r FIG. 6. 9O 92 ATTY.

Feb. 14, 1967 A. o. SYKES 3,304, 534

MULTIPURPOSE PIEZOELECTRIC TRANSDUCER SYSTEM Original Filed Feb. 27,1963 4 Sheets-Sheet 5 PIEZOELECTRIC CHANNE ELEMENT Ll 8 2 J 439PIEZOELECTRIC ELEMENT |CHANNEL 2 RL INVENTOR.

ALAN O.SYKES TTY.

United States Patent 3,304,534 MULTIPURPOSE PIEZOELECTRIC TRANSDUCERSYSTEM Alan 0. Sykes, Fairfax County, Va. (304 Mashie Drive, Vienna, Va.22180) Original application Feb. 27, 1963, Ser. No. 261,549. Divided andthis application Aug. 16, 1965, Ser. No.

Claims. (Cl. 340-10) The invention described herein may be manufacturedand used by or for the Government of the United States of America forgovernmental purposes without the payment of any royalties thereon ortherefor.

The present application is a divisional application of applicantscopending application Serial No. 261,549, filed February 27, 1963.

The invention relates to a transducing system and more particularly to apiezoelectric transducing system capable of providing accuratemeasurements of several different parameters and pairs of certainparameters simultaneously.

Heretofore, transducer measuring systems and devices have been limitedto a single measurement capability or have been inaccurate underunfavorable measuring conditions. For example, one system may beprovided for the sole purpose of measuring sound pressure; anotherseparate system, acceleration; yet another system, pressure gradient,and so on. Consequently, in order to provide measurement of severaldifferent parameters, several different corresponding systems arerequired. Moreover, under conditions of high ambient noise and othersources of extraneous signals, accuracy decreases.

A further difficulty corollary with each type of singleparametermeasuring system is that while the system transducer is desirablysensitive to acceleration, such a transducer may also be unfortuitouslysensitive to sound pressure. Being sensitive to both influences, suchsystems used in mixed environments such as sea water produce confusedand inaccurate measurement data. Further, those sound measuring systemsdesigned to have low sensitivity to acceleration are capable ofmeasuring sound pressure only. Conversely, acceleration measuringsystems designed for low sensitivity to sound pressure measure onlyacceleration.

The present invention provides novel transducers and a transducer systemarrangement whereby the above-mentioned prior art difiiculties andlimitations of measurement are overcome. Briefly, according to anembodiment of the present invention, there is provided novelpiezoelectric transducing means for producing two different outputparameters. The two different output parameters are processed by meansof electronic circuitry so that both outputs provide simultaneousmeasurement data of different parameters. In another embodiment, circuitmeans are provided to effect cancelling of one of the outputs so thatthe fidelity (i.e. signal to noise ratio) of the desired output data isincreased. Novel circuit means are also provided for increasing theaccuracy of measurement signals including accurate pressure gradients.

Accordingly, it is an object of the present invention to provide asystem for simultaneously measuring sound pressure and acceleration, andfor simultaneously measuring sound pressure and pressure gradient.

Another object of this invention is to provide a system to measure soundpressure which is insensitive to acceleration and vice versa.

Another object of this invention is to provide a system for measuringacoustic intensity.

Yet another object of the present invention is the provision of atransducer having high acoustic sensitivity.

ice

Another object of this invention is to provide a piezoelectric absolutedisplacement gage.

Still another object of this invention is the provision of amultipurpose piezoelectric transducer measuring system of improved noveldesign capable of withstanding high static pressures and suitable foruse as a microphone or hydrophone.

Another object of this invention is to provide increased accuracy oftransducer measurements by means of novel signal processing circuitry.

The foregoing and other objects, features and advantages of the presentinvention will be better understood by referring to the" accompanyingdrawings in which:

FIGS. 1-7 and 12 are views in cross section of various illustrativeembodiments of piezoelectric transducers according to the invention;

'FIG. 8 is a schematic diagram of a transducer measuring systemaccording to an embodiment of the present invention.

FIG. 9 is an explanatory block diagram illustrating particle velocitymeasurement;

FIG. 10 is a schematic block diagram of an embodiment incorporatingimproved circuit means according to the invention for providing accuratemeasurements; and

FIG. 11 is an explanatory diagram illustrating the principles of anembodiment of the invention in connection with use thereof as anabsolute displacement gage.

Referring to the drawings in which like reference numerals indicate likeparts, there is illustrated in FIG. 1 a cross sectional view of acylindrically symmetric transducer 1 1 having a heavy metallic centralmounting disc 13. The mounting disc 13 has holes 15 for attaching thetransducer 11 rigidly to a test specimen. A pair of piezoelectric discs17 and 19, each with an electrode such as a conductive coating on eachof their flat surfaces, are separated from each other by glassinsulating discs 23 which are mounted on opposite sides of the centralmounting disc 13.

The transducer 11 is further formed of a pair of opposing, identical,rigid, cylindrical, metallic housings 25 and 26. The housings 25-26 eachhave stiif, flat end portions 25a and 26a effectively in vibratingcontact wit-h the crystals 17 and 19. Each flat end portion has a largesurface area compared with the surface area of its adjacentpiezoelectric crystal element. Each housing is secured to the centralmounting disc 13 by means of soft screws 27 extending through the discs23 and piezoelectric elements and secured into the central mounting disc13. The screws 27 may be made of nylon, and they have negligiblestiffness compared with that of the piezoelectric elements 17 and 19. Awatertight seal for the transducer 11 is provided by O-rings 29 ofstiffness small compared with the piezoelectric elements and seated inannular grooves 31 in the opposed housings 25 and 26 so that when thescrews 27 are brought home, the O-rings are squeezed between thehousings 25 and 26, and the central mounting disc 13. The O-rings arepreferably positioned as far outward from the axis of symmetry aspossible to enhance stress multiplying effects of the housings 25, 26 onthe crystal elements 17 and 19.

Each of the leads 21 has an electrode such as a conductive coating onthe flat surfaces of the respective piezoelectric discs 17 and 19. Eachlead 21 passes watertightly through the housings 25 and 26 of thetransducer for connection to the novel signal processing equipmentaccording to the invention.

The two piezoelectric elements 17 and 19 are closely matched to provideequal capacity and equal piezoelectric constant. The transducer of theinvention has an acoustic sensitivity much greater than the sensitivityattributable to the acoustic sensitivities of the piezoelectric elements17 and 19 alone. Stress multiplication is provided by virture of thevibration contact of the large area flat end portions of the housings 25and 26 with the smaller surface areas of the piezoelectric elements.Specifically, the stress appearing on each respective flat surface ofthe piezoelectric elements 17 and 19 at measurement frequencies ofinterest is equal to the applied acoustic pressure multiplied by theratio of the area of the outer surface of one housing to the projectedarea of one surface of one of the piezoelectric elements on a planeperpendicular to the axis of symmetry, Le. a plane perpendicular to theend portions of the housings Z5 and 26 and to the flat surfaces of thepiezoelectric elements 17 and 19.

When the transducer 11 is placed in a sound field of frequencies havingwavelengths much larger than the thickness of the transducer measuredparallel to its axis of symmetry, both piezoelectric elements 17 and 19will experience stresses of the same sign. That is, both will besimultaneously in tension or compression. However, when excited byvibrations of the central mounted disc 13 parallel to the axis ofsymmetry, the piezoelectric elements experience stresses of oppositesign.

Since the sign of the electric signals generated by the piezoelectricelements is determined by the sign of the stress, it is thereforepossible to combine the two voltages in such fashion that they add foran applied sound pressure and subtract for an applied vibration, or viceversa.

Thus, both sound pressure and acceleration or displacement due tovibration can be obtained with the same transducer if the outputs of thetwo piezoelectric elements 17 and 19 are both added and subtracted. Toaccomplish this, it is necessary that the capacities and piezoelectricconstants of the two elements 17 and 19 be equal Any slight variationsin the piezoelectric constants may be further compensated for byelectrical means, and variations in capacity may be corrected byadjusting the size of the piezoelectric elements or by means of trimmingcapacitors.

Referring to FIG. 8, there is provided as shown therein an electroniccircuit for equalizing the sensitivities of the two piezoelectricelements 17 and 19 to provide cancellation of signals due to extraneousinfluences. The circuit of FIG. 8 may also simultaneously producesignals proportional to the sum and difference of two respective inputsignals ep and ep produced by the piezoelectric elements 17 and 19.

The circuit of FIG. 8 includes channel 1 and channel 2 input paths forreceiving signals ep and ep respectively from the piezoelectric elements17 and 19 when excited. The signals ep and ep are passed through animpedance matching R/C network 35, and are then fed to respective gridsof a pair of matched triodes 37 and 39.

Because there may be inequalities in the piezoelectric constants of thetwo piezoelectric elements 17 and 19, gain adjusting means are providedto balance channels 1 and 2. For example, e may unfortuitously exceed epin magnitude when ep and CD2 are in phase due to excitation from acommon stimulus.

The gain adjusting means include a pair of variable resistances R and Rconnecting the cathodes of the respective triodes 37 and 39 to a commonjunction 41. The junction 41 is connected through a resistance R to asource of negative reference voltage, B- and through a capacitor 43 toan output terminal 45.

The remainder of the circuit includes a source of positlme referencevoltage B+ connected through a resistance m to the plate of triode 39and through a resistance R to the plate of triode 37. An output terminal47 is connected to the plate of triode 37 in parallel with said sourceof B+ When the unequal in-phase signals ep and em are applied to thegrids of the respective triodes 37 and 39,

the resistance R may be adjusted so that the current flowing through Ris zero.

If now the leads 21 to one of the piezoelectric elements are reversed sothat the two signals ep and @12 are out of phase, with their magnitudesunchanged, R may be adjusted so that the current flowing through R iszero.

For convenience, the channel 1 and 2 signals respectively may bedesignated as where e is the sound pressure signal of piezoelectricelement 17, 6P2 is the sound pressure signal of element 19.

The conditions necessary for accurate measurement of the pressuregradient are:

where c is the speed of sound waves in the medium, r is the distancefrom the source of sound waves to the pickup or transducer 11, w=21rf, fbeing frequency, and Ar is the distance between the two piezoelectricelements such as 17 and 19.

If p is the pressure measured at r, Sp is the pressure sensitivity ofthe transducer at r and r-i-Ar, Ar being the distance between the twopiezoelectric elements, and ep -ep is the difference in voltage phasorsof the signals from the piezoelectric elements 17 and 19, then, underthe foregoing conditions, it can be shown that Under the same foregoingconditions, the particle velocity U at the distance r may be obtained byintegrating the difference signal ep ep as shown in FIG. 9. Any suitableintegrating circuit 55 having a gain of A and a time constant RC may beemployed. The output s of the integrator 55 is:

172 n A t'wRC The particle velocity U can be shown to be:

c 5) (sc being the acoustic resistance of the medium).

It can be shown that:

Therefore, the particle velocity is given by where wAT 2 That is, forexample, where the piezoelectric elements. are further apart and thesource is closer to the trans- PSDUI ducers. Under these conditions, itcan be shown that the diflference in voltage phasors,

g tea eries-a re eer which lead to considerable error in the outputsignal, must be eliminated. To accomplish this, the followingmathematical steps are carried out by the following correspondingelements of the circuit of FIG. 10.

In an amplifier 59 having a gain and is eliminated from the right sideof Equation 8 to produce an ouput e Thus,

Men-e-eniieeeri The signal c is fed to a diiferentiating amplifier 60having an R C time constant and a gain of A to produce an output signale Thus,

e iwe A R C The signal e is fed to a second differentiating amplifier 61having a gain of A and a time constant of R C to produce an output e Thegains A A and associated time constants are related thus:

The signal e is difierentiated at difierentiating amplifier 63 having again of A and a time constant of R 0 producing e so that A signal e isproduced at a summation device 65 of any suitable design by taking thesum of the signals e and e, applied thereto. Thus,

-w Ar 2 ,w Ar T T n 7 13) 6 The signal e is fed to an amplifying device67 of any suitable design and having a gain of A =e to produce a signale so that It is seen that the signal e possesses the terms to beeliminated-- WW Z 6 c i 2 c By additively combining the signals e and eto produce an output signal e the undesired terms leading to measurementinaccuracies are eliminated. A summation device 69 of any suitabledesign additively combines the signals e and e to produce an output eThus,

By integrating the e signal in a suitable integrating device 71 having again of A and a time constant of R C the following output signal e isobtained.

e, is the acceleration signal of element 17, and 2 is the accelerationsignal of element 19.

With the resistances R and R adjusted, and with each piezoelectricelement being subjected to both sound pressure through the housings andacceleration (vibration) through the central mounting disc, a signalproportional to the acceleration of the central mounting disc willappear across R at the output of channel 1, and a signal proportional tothe sound pressure will appear across R Since by adjustment, e =e andsince e,, =e by adjustment of R and R (provided the accelerationsensitivities of the transducer elements are equal), ther is obtained anacceleration signal:

and the sound pressure:

Obviously, by performing the adding operation in channel 1 only or thesubtracting operation in channel 2 only, either of the two outputsignals 22 or Ze is obtained without interference from the other signal.

Under certain conditions, the circuit of FIG. 8 may also be used toobtain both the pressure and pressure gradient. If the transducer 11 issuspended in a sound field and isolated from all vibratory excitation, apressure sum signal may be obtained from measuring across R and a signalproportional to the diiference in two pressures experienced by thepiezoelectric elements 17 and 19 obtained across R A second outputsignal, 2,, is obtained by amplifying e51 directly in a suitable device73 having a gain of A QJ'ZA'TEPI From Equations 3 and 15, it followsthat:

dp/a r=e /Al-S (19) 7 From Equations and 1 6 t'wr Ar 1 Ar P A 1 eR4C4eD1Afi cm? R404 Sp 11 The particle velocity M at r is thereforegiven by where 0 is the phase angle between pressure and velocity.

It follows from Equation 17 that ei A Sp Thus, P and 2 are in phase.Therefore, the acoustic intensity I may be expressed as The presentinvention affords the measurement of acoustic intensity I by measuring ee; and the phase angle therebetween, and substituting the valuestherefor in Equation 24 above, and the resulting multiplication may becarried out electronically by any suitable well known means.

In measuring pressure gradient it is essential that the bulk of thetransducer weight be concentrated in the center disc mounting 13 whichshould be at least several times heavier than the total weight of allother components of the transducer 11. If the disc 13 were to have nomass, the difference signal epg-ep would unfortuitously be zero.

Reference is now made to FIGS. 3, 4 and 6 which illustrate variousembodiments of the transducer having a relatively heavy central mountingpieces similar to the heavy central mounting disc 13 of FIG. 1.

The transducer of FIG. 3 is provided with transducer isolation means.Unlike the transducer shown in FIG. 1, that of FIG. 3 has centralmounting piece in the form of a thick disc 75 coextensive with thehousings 25, 26 and suitably sealed thereto by O-rings 2%. The disc '75has a peripheral groove 77 for receiving an fiat annular flexiblediaphragm 79 having mounting holes 81. The diaphragm 79 effectivelyisolates the transducer from local vibrations. The natural frequency ofthe transducer of FIG. 3 is much lower than that of FIG. 1, and thusdoes not respond to acceleration forces at frequencies which are muchlower than the lowest frequency of interest for measurement purposes.Consequently the transducer of FIG. 3 is especially useful for measuringsound pressure gradients and sound pressure in an unfavorableenvironment. Also, by virtue of the isolation and if properly connected,it can be used as a piezoelectric absolute displacement gage.

The transducer embodiment of FIG. 4 includes a pair of annularpiezoelectric elements 83 and 85 opposingly supported by a heavy centralmounting disc 87. The disc 87 has a pair of opposed shoulders 89 spacedfrom a pair of identical opposing transducer housings 90 so that O-rings91 may be squeezed between the shoulders 89 and the identical housings90 to provide a seal. The elements 83 and 85 are insulated from the disc87 and housings 90 by thin insulating discs 92. The transducer of FIG. 4is similar in operational advantages to that of FIG. 1, and theremaining elements of the FIG. 4 transducer have the same purpose as thecorrespondingly designated structural elements of the transducer ofFIG. 1. The transducer of FIGS. 1 and 4 are both particularly useful asaccelerometers.

The transducer embodiment of FIG. 6 is very similar to that of FIG. 4except central mounting disc 87 is cos 0 thinner for a differentfrequency sensitivity. A single screw )7 secures together identicaltransducer housings and the remaining intervening transducer elements.Instead of an O-ring seal, the sealing of the transducer of FIG. 6 iscarried out by means of compliant sealing elements as which are suitablybonded to; opposing surfaces of the shoulders 39 and the housings 90'.

The transducer-s of this invention as embodied in FIGS. 2 and 5 employonly a single piezoelectric element and are not provided with a heavycentral mounting disc such as element 13 of FIG. 1. In FIG. 2 a singlescrew 97 secures together the transducer housings 25, 26 in squeezingrelationship against an O-ring 29 and a single discshaped piezoelectricelement 101.

The transducer of FIG. 5 has an annular piezoelectric element 192 andfurther includes a pair of opposed thick disc like housings 103 and 195.The housing 1433 has thin, short peripheral cylindrical wall 107exttending toward the housing 1495. The housing has an inner annularshoulder 109 extending toward housing 103 and juxtaposed to thecylindrical wall 107. The transducer of FIG. 5 is sealed with acompliant seal such as rubber or polyurethane bonded to the wall 107 andto the shoulder m9.

In FIG. 7 another embodiment of the transducer similar to those of FIGS.2 and 5 is shown having two piezoelectric elements 111 and 113 in theform of discs. The elements 111 and 113 are insulatedly separated fromeach other and from the housings by discs 23 made of suitable insulatingmaterial such as a hard plastic or glass. The transducer of FIG. 7 isotherwise assembled in the same manner as that of FIG. 2.

Referring to FIG. 12, there is shown yet another embodiment of atransducer wherein the O-rings or compliant sealing means areeliminated. The transducer of FIG. 12 is provided with a pair of rigididentical flat cylindrical (or square or rectangular) housing members115 which are flat on all surfaces perpendicular to the axis ofsymmetry. An annular or perimetrical piezoelectric crystal element 117having electrically conductive coatings thereon is suitably welded orbonded in a stiff manner to each of a pair of glass insulating elements119. Suitable leads (not shown) are provided for by the crystalelements. The insulating elements 11s are suitably bonded to thehousings 115. Although the insulating elements of FIG. 12 areillustrated as extending completely across the extent of the transducer,alternatively the insulating elements may obviously be of even dimensionand shape with the piezoelectric element 117. This applies to the otherillustrated embodiments as well. A nylon or other soft screw 121 extendsalong the axis of symmetry to further press the transducer elementstogether.

The transducer of FIG. 12, assembled as explained above, is thenimmersed in a suitable compliant scaling compound and the compoundallowed to harden. The result is a completely sealed transducer unitsuitable for underwater use and capable of withstanding high staticpressure. Moreover, the elimination of discrete sealing means evenfurther decreases any measurement errors due to the interaction offorces between resilient sealing means and inertia of water beingdisplaced.

The transducers embodied in FIGS. 2, 5 and 7 are particularly usefulwhere vibration (acceleration) measurements are not required, such asfor sound pressure measurements alone.

The transducers of FIGS. 1 and 4 are particularly useful aspiezoelectric accelerometers, while those of FIGS. 3 and 6 are intendedfor use as piezoelectric displacement gages in that they are resilientlydamped or spring mounted. Of course, they can also measure both soundpressure and displacement simultaneously or just sound pressure alone.

Measurement of piezoelectric displacement may be carried out in thefollowing manner. Referring to FIG. 11,

9 a simple mass-spring system is diagrammatically shown with a springwith spring constant K and a mass M representatively positioned atterminals 1 and 2.

If there be applied at terminal 1 a vibratory displacement it can beshown that the ratio of the displacement phasor X at terminal 2 to thedisplacement phasor X at terminal 1 is where W =K/M and -W X is theacceleration of the mass M. It follows from Equation 26 that As anaccelerometer, the transducer of FIGS. 3 and 6 will produce an outputsuch that where is the sensitivity of the accelerometer in volts perunit of acceleration.

Thus, the sensitivity S of the spring-mounted accelerometer as adisplacement gage is The transducers of FIGS. 3 and 6 accomplish doubleintegration effectively and thus act as absolute displacement gages inaddition to being employed as sound pressure cancelling displacementgages, or gages from which both the displacement and sound pressure canbe obtained. The foregoing displacement provides measurements relativeto an inertial frame of reference, not a fixed point in space.

It is to be understood that the transducer system of the presentinvention provides sound pressure information relatively uninfiuenced bymotion of the transducer, or displacement or acceleration informationrelatively uninfiuenced by the pressure of sound field; or it canprovide both, either displacement or acceleration, and sound pressureinformation simultaneously. The transducers themselves need not becylindrically symmetrical, but may alternatively be square orrectangular or some other shape having an axis of symmetry.

Moreover, the system of the present invention provides sound pressureand sound pressure gradient information simultaneously at essentiallythe same point in space, or sound pressure and particle velocityinformation U from which the acoustic intensity I can be calculated.

Obviously many modifications and variations of the present invention arepossible in the light of the above teachings. It is therefore to beunderstood that within the scope of the appended claims the inventionmay be practiced otherwise than as specifically described.

What is claimed is:

1. A transducer system for providing an output signal representingaccurate measurement of input signal parameters under conditions whichwould normally lead to inaccuracies due to presence of second and thirdorder error terms in the transducer output signals, comprising;transducer means having first and second piezoelectric elements mountedfor response to input signal parameters at least one of which is soundpressure to produce outputs represented by voltage phasors e and erespectively;

the signal difference between voltage phasors e and e of the respectiveoutput signals of the piezoelectric elements having second and thirdorder signal error components herein;

means for subtracting one said voltage phasor from the other therebyproducing said signal error components in the signal e e signalprocessing means for deriving from said one voltage phasor said signalerror components;

and means for algebraically combining the subtracted signals with saidone voltage phasor derived signal containing said signal errorcomponents to thereby eliminate said signal error components from thesubtracted signals e -e 2. The system as defined according to claim 1but further characterized by said transducer means comprismg:

a pair of sound-pressure responsive housings each having a fiat rigidend portion in insulated vibrating contact with one fiat surface of acorresponding one of said piezoelectric elements; the area of said flatend portion being greater than the opposing surface area of thecorresponding piezoelectric element; central mass element responsive tovibrations of a different frequency than said housings and locatedbetween said housings and between said piezoelectric elements ininsulated vibrating contact with the other flat surfaces of saidpiezoelectri celements;

means for sealably securing said housings toward each other and towardsaid central mass element to provide a closed and sealed hollowtransducer body.

3. The system as defined according to claim 1 but further characterizedby said transducer means comprismg:

a pair of sound-pressure responsive housings each having a flat rigidend portion in insulated vibrating contact with one flat surface of acorresponding one of said piezoelectric elements, the area of said flatend surface being greater than the opposing flat surface area of thecorresponding piezoelectric element to thereby obtain stressmultiplication of vibrational movements of said housings through saidrespective piezoelectric elements;

and means for sealably securing said housings together to form afluidtight and hollow transducer body.

4. The system as defined according to claim 1 but further characterizedby said output signal being sound pressure gradient.

5. The system as defined according to claim 1 but further characterizedby integrating means coupled to receive the output of the algebraiccombining means for producing an output signal representative of theparticle velocity u at the transducer location.

6. The system as defined according to claim 1 but further characterizedby said signal deriving means including circuit means for amplifyingsaid error signal components, a second circuit means for amplifying saidone voltage phasor, whereby an output signal representative of theacoustic intensity I may be obtained.

7. The system as defined according to claim 1 but further characterizedby said transducer means comprising vibration isolation mounting meansconnected to said heavy mass element, whereby the system output signalis representative of absolute displacement.

8. A transducer system for providing an output signal representingaccurate measurement of input signal parameters under conditions whichwould normally lead to 1 l inaccuracies due to presence of second andthird order error terms in the transducer output signals comprising:transducer means to produce outputs represented by voltage phasors e ande respectively; the signal difference between voltage phasors e and ehaving second and third order signal error components therein; means forsubtracting one said voltage phasor from the other thereby producingsaid signal error components in the signal e e signal processing meansfor deriving from said one voltage phasor said signal error components;and means for .alge'brically combining the subtracted signals with saidone voltage phasor derived signal error components to thereby eliminatesaid SE31 error components from the subtracted signals e No referencescited.

RODNEY D. BENNETT, Acting Primary Examiner. CHESTER L. JUSTUS, Examiner.

B. L. RIBANDO, Assistant Examiner.

1. A TRANSDUCER SYSTEM FOR PROVIDING AN OUTPUT SIGNAL REPRESENTINGACCURATE MEASUREMENT OF INPUT SIGNAL PARAMETERS UNDER CONDITIONS WHICHWOULD NORMALLY LEAD TO INACCURACIES DUE TO PRESENCE OF SECOND AND THIRDORDER ERROR TERMS IN THE TRANSDUCER OUTPUT SIGNALS, COMPRISING;TRANSDUCER MEANS HAVING FIRST AND SECOND PIEZOELECTRIC ELEMENTS MOUNTEDFOR RESPONSE TO INPUT SIGNAL PARAMETERS AT LEAST ONE OF WHICH IS SOUNDPRESSURE TO PRODUCE OUTPUTS REPRESENTED BY VOLTAGE PHASORS EP1 AND EP2RESPECTIVELY; THE SIGNAL DIFFERENCE BETWEEN VOLTAGE PHASORS EP2 AND EP1OF THE RESPECTIVE OUTPUT SIGNALS OF THE PIEZOELECTRIC ELEMENTS HAVINGSECOND AND THIRD ORDER SIGNAL ERROR COMPONENTS HEREIN; MEANS FORSUBSTRACTING ONE SAID VOLTAGE PHASOR FROM THE OTHER THEREBY PRODUCINGSAID SIGNAL ERROR COMPONENTS IN THE SIGNAL EP2-EP1; SIGNAL PROCESSINGMEANS FOR DERIVING FROM SAID ONE VOLTAGE PHASOR SAID SIGNAL ERRORCOMPONENTS; AND MEANS FOR ALGEBRAICALLY COMBINING THE SUBTRACTED SIGNALSWITH ONE VOLTAGE PHASOR DERIVED SIGNAL CONTAINING SAID SIGNAL ERRORCOMPONENTS TO THEREBY ELIMINATE SAID SIGNAL ERROR COMPONENTS FROM THESUBTRACTED SIGNALS EP2-EP1.